Taxation and The Life Cycle of Firms

Andres Erosa

Beatriz Gonzalez ∗

This version: October 2018

Abstract

The Hopenhayn and Rogerson (1993) framework of firm dynamics is extended to

understand how different forms of taxing capital income affect investment and financial

policies over the life cycle of firms. Relative to dividends and capital gains taxation,

corporate income taxation slows down growth over the life cycle by reducing after-

tax profits available for reinvesting in the firm. It also diminishes entry by negatively

affecting the value of entrants relative to the that of incumbents firm. After a tax

reform eliminating the corporate income tax in a revenue neutral way, output and

capital increase by 13% and 35%. The large response of firm entry to the tax reform

is crucial for our results.

Keywords Macroeconomics, Taxation, Firm Dynamics, Investment

JEL Codes D21, E22, E62, G12, G32, G35, H25, H32

∗Universidad Carlos III de Madrid, Departamento de Economıa, Calle Madrid 126, 28903 Getafe, Madrid.Beatriz gratefully acknowledges financial support by ’La Caixa’ Foundation.

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1 Introduction

The macroeconomic effects of the taxation of capital income have received a great deal of

attention by economists and policy makers. Throughout modern economies the taxation of

capital income takes many different forms: capital gains taxation, interest income taxation,

dividend taxation, and corporate income taxation. In particular, the tax rate on corporate

income in the US was until recently among the highest among OECD countries and this

has raised concerns about its effects on job creation and investment. Policy advisors from

the Obama and Trump administration have advocated for changes in the taxation of capital

income and, indeed, the Trump administration has recently cut by nearly a half the corporate

income tax rate. In this paper, we study how different forms of taxing capital income affect

investment and financing decisions of firms over their life cycle, as well as the creation of new

firms (firm entry), aggregate capital accumulation and output. We then evaluate the effects

of a tax reform that eliminates the tax on corporate income and replace the lost revenue

with a common tax rate on all other form of capital income.

Corporate profits distributed as dividends suffer the so-called ‘double taxation’, since

they are taxed both at corporate and personal income levels (by the corporate income tax and

the divident tax, respectively). The literature has long emphasized that corporate income

taxation diminishes investment by firms by reducing the after tax return on capital. In this

paper, we show that these distortions are much more severe when firms’ growth over the

life cycle is constrained by financial frictions. We also show that the impact of dividend

taxation on firm investment decisions critically depend on the stage that firms are in their

life cycle, as young firms are more likely to issue equity and old firms are more likely to issue

dividends. Young firms behave according to the traditional view’ in the finance literature that

focuses on how raising the cost of equity finance (dividend taxation) negatively affects firms’

investment.1 However, as emphasized by the ‘new view’ in the finance literature, dividend

taxation does not affect investment decisions of firms distributing dividends (mature firms)

since the dividend tax leads to an equiproportional reduction in the return and costs of

investment. More generally, our paper stresses that the various ways capital income can be

taxed (whether corporate income, dividend, or capital gains taxation) have quite different

effects on investment and payout policies over the life cycle of firms, and hence on the

life cycle growth of firms. They also have different and asymmetric effects on the market

valuation of new versus incumbent firms and thereby on firm entry.

Our paper is motivated by micro evidence on firm dynamics and the life cycle of

1See, for instance, (Auerbach, 2002) for a description of these views. Empirical findings on this issueare mixed. For instance, Poterba and Summers (1985) find evidence supporting the traditional view usingBritish data. Kari et al. (2009) find evidence supporting more the new view using Finnish data. Auerbach andHassett (2007) found that in the US, firms behave according to both views, which points at the coexistenceof both regimes in the data.

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firms. Haltiwanger et al. (2013) argue that start ups play a critical role for understanding

US employment growth dynamics. The mass of firms entering the economy is large, most

new businesses start as small but (conditional on survival) grow fast, and new entrants

are important for understanding employment growth. Moreover, Hsieh and Klenow (2009)

argue that the cross country differences in the life cycle growth of firms are important for

understanding aggregate productivity differences across countries. The evidence indicates

that firms face substantial equity issuance costs (see Hennessy and Whited (2007), Lee et al.

(1996)). Using micro evidence from US and UK firms, Cloyne et al. (2018) show that

financial frictions affect more strongly investment decisions of young firms than of mature

firms. Campbell et al. (2013) empirically document heterogeneous investment responses

across young and mature firms after the reduction on shareholder taxes in the US in 2003.

Becker et al. (2013) study many tax reforms on 25 countries over a 20 year period, finding

that changes in payout taxes affect firms differently depending on their financial regime.

Overall, we believe that the evidence points to the importance of modeling the life cycle

of firms for assessing the effects of taxation. A model with a representative firm, as in

the standard Neoclassical Growth Model, implicitly focuses on mature firms (i.e. those

distributing dividends where the ‘new view’ holds) disregarding the evidence that investment

responses to tax changes vary over the life cycle of firms. Moreover, the empirical findings

of Haltiwanger et al. (2013) suggest that it is important to consider the impact of taxation

on business entry.

We extend the Hopenhayn and Rogerson (1993) framework of firm dynamics to under-

stand how different forms of taxing corporate income affect the life cycle of firms. We start

by analysing a simple version of the model with a deterministic fixed level of productivity

determined upon entry. Companies need to raise equity to set the firm up, starting their life

in the ‘traditional view’ regime (equity issuance phase). They grow by accumulating profits

(growing phase), until they reach their optimal size and start distributing dividends (matu-

rity phase). Consistently with the ‘new view’, dividend taxation does not distort investment

decisions and dividends paid by mature firms. However, dividend taxation diminishes the

optimal amount of initial equity issued by firms. Intuitively, firms can diminish the taxes

paid by financing a larger portion of investments with retained earnings. Hence, dividend

taxation reduces the initial size of firms, retarding the age at which they reach maturity, and

diminishes entry. The taxation of capital gains have opposite effects from dividend taxation.

First, the taxation of capital gains encourages firms to issue more equity at entry in order to

avoid paying the taxes that would accrue with the accumulation of internal funds. Second,

it distorts the optimal scale of the firm at maturity. Corporate income taxation impacts on

capital accumulation through several channels. First, corporate income taxation distorts the

optimal size and dividends paid by mature firms by decreasing the return on capital. Second,

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crucial to our analysis and results, the corporate income tax decreases after-tax earnings,

making it harder for firms to finance investment with retained earnings and causing firms

to grow at a slower pace over their life cycle. As a result, the market value of the firm

decreases, leading to two additional effects of corporate income taxation on capital accumu-

lation: Firms raise less equity at entry and the equilibrium mass of entry becomes smaller.

While these effects are also present under dividend taxation, we find that they are stronger

under corporate income taxation.

The baseline economy with firm dynamics (due to idiosyncratic productivity shocks

at the firm level) is calibrated to moments on the micro data on firms’ investment and

financing decisions. We use the calibrated model economy to quantitatively assess the effects

of a reform that eliminates the taxation of corporate income while keeping constant the tax

revenue collected on capital. This is done by finding the common tax rate (τ) on all forms

of capital income (dividends τd, interest income τr, and capital gains τg) that collects the

same tax revenue as in the baseline economy. The purpose of the proposed policy reform is

twofold. Firstly, by equating the three tax rates we would be treating symmetrically all forms

of capital income from the household perspective. Secondly, by eliminating the corporate

tax, we allow financially constrained firms to accumulate profits and to reach maturity (the

dividend distribution stage) faster. Since under our proposed reform firms face higher taxes

on dividend distribution, the tax burden shifts from constrained firms (firms with high

marginal valuation of capital) to unconstrained firms (firms with low marginal valuation of

capital). We find that the elimination of the corporate income tax in the baseline economy

(τc = 0.34) should be accompanied by an increase in the other capital income tax rates to

0.39 in order to keep government revenue constant (the dividend and capital gains tax in the

baseline economy were set to 0.15 and the interest income tax was set to 0.25). This revenue

neutral tax reform leads to an increase in aggregate output of 13.6%, which is accompanied

by a large increase in the aggregate capital stock (35%) and in the number of firms (39.3%).

Note that the fact that aggregate capital and output rise less than the number of firms

indicates that the average size of firms is smaller after the tax reform. Hence, the large

response of firm entry to the tax reform drives the large increase in aggregate output and

capital.

At the heart of our results is that the tax reform increases more the expected value at

entry than the value of incumbent firms, leading to a reallocation of resources from mature

to younger firms, that operates through an increase in entry and in the equilibrium wage

rate. The elimination of corporate income taxation allows financially constrained firms to

retain a larger fraction of their earnings and increase their investments. The ability to retain

earnings is particularly relevant for young firms, which are more likely to be constrained than

the average incumbent firm in the economy. Since the value at entry is determined by the

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average value of age-0 firms, we find that the value of the average firm entering the economy

increases more than that of incumbent firms when corporate inome taxation is eliminated.

In general equilibrium, the increase in the value of entry requires the wage rate to rise, which

reduces labor demand by incumbent firms. Labor market clearing requires a larger mass of

firm entry, which rises by about 39.3%. Larger firm entry, together with a reallocation of

resources to financially constraint firms, lead to an increase in aggregate TFP of 5.2%.

Our model economy builds on Gourio and Miao (2010), who study the impact of divi-

dend taxation on firms investment and payout decisions. We contribute by comparing alter-

native forms of capital income taxation and by extending their analysis to incorporate three

key features for our results: life cycle (endogenous entry), financial frictions, and corporate

income taxes. In particular, we emphasize the importance of the life cycle of firms for un-

derstanding how taxation affects investment incentives of firms. Korinek and Stiglitz (2009)

build a theory of the life cycle of firms for understanding the impact of dividend taxation but

abstract from corporate income taxation and firm entry. McGrattan and Prescott (2005)

and Atesagaoglu (2012) study how corporate income taxation affect the market valuation

of firms in environments with a representative firm. Conesa and Domınguez (2013) advo-

cate for the elimination of corporate income taxation in a Ramsey optimal taxation exercise

with a representative firm, with no financial frictions and no firm entry/exit. Similar to us,

Anagnostopoulos et al. (2015) evaluate the gains of eliminating corporate income taxation in

a model with firm heterogeneity and household heterogeneity. We abstract from household

heterogeneity but contribute by focusing on firm entry and the life cycle of firms, which turn

out to be key for the large quantitative effects of our tax reform and which Haltiwanger

et al. (2013) emphasize as crucial for understanding the dynamics of employment growth in

the US. The financial crises has sparked the importance of the literature analyzing the role

of financial frictions in business cycle fluctuations. Papers in this literature include Coo-

ley and Quadrini (2001), Khan and Thomas (2013), Jermann and Quadrini (2012) (among

many others). Our results suggest that the design of capital income taxation may affect the

propagation of business cycle shocks.

An outline of the paper follows. In Section 2 we present and analyze simple version

of our baseline model economy in which firms do not face idiosyncratic shocks to their

productivity. We use it to illustrate how different forms of taxing capital income affect

investment and payout policies over the life cycle of firms, the value of firms to its share

holders, and firm entry. In Section 3 we present our baseline model economy of firm dynamics

and taxation of capital income, calibrate it, and perform our main quantitative exercise. We

evaluate a tax reform that eliminates corporate income taxes while keeping constant revenue

from capital income. We analyze its impact on macroeconomic aggregates as well as on firms

decisions on investment and payout policies over the life cycle. Section 4 concludes.

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2 A Simple Deterministic Model Economy

Our baseline model extends the Hopenhayn and Rogerson (1993) framework of firm dynamics

to study taxation of corporate capital income. Time is continuous. Each firm may exit the

economy with some fixed probability. The entry of new firms is endogenous. Firms can

finance investment with retained profits, equity issuance, and debt. Firms face adjustment

costs in capital. Following Cooley and Quadrini (2001) and Gomes (2001), firms face financial

frictions: borrowing is limited by a collateral constraint and equity issuance is costly. There

is a representative household that owns all firms. There is a large number of firms so that

the representative consumer does not face any uncertainty. As in Gourio and Miao (2010),

households pay taxes on dividends (τd), interest income (τr), and capital gains taxes (τg).2

In addition, corporations pay taxes on corporate profits (τc) so that capital income is taxed

both at the firm and household level.

In this section, we illustrate the key ideas in our paper in deterministic version of our

baseline model economy that abstracts from adjustment costs in capital.

2.1 The problem of a firm.

We assume that when firms are created, they draw a productivity z that stays fixed over

the lifetime of a firm. Firms exit exogenously the economy at a rate δd. The economy is a

steady state with an after tax interest rate equal to r(1− τr) = ρ, where ρ is the rate of time

preference of the representative household (investor).

Each firm produce output with a decreasing returns to scale production function in

capital and labor inputs: f(z, k, n) = z1−α−ηkαnη. Profits are given by

π(z, k) = maxn{f(z, k)− wn− δk}

The flow constraint is

k = (1− τc)π(z, k)− d+ (1− ξ)e,

where d and e denote dividend distribution and equity issued by firms. We assume that equity

issuance is costly. There is a cost ξ per unit of equity issued, so the resources available are

e(1− ξ).Consider a firm with fix z. The market value (V ), the dividends( d) paid, and the

equity issued e are deterministic functions of the age of the firm t. However, we do not

2While in the US capital gains are taxed upon realization, we follow standard practice in the literature bymodeling capital gains taxation on an accrual basis. This modeling choice simplifies the analysis considerableand allow us to derive our results in a more transparent way.

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explicitly index these variables with a subscript t to simplify the notation (unless there is

some risk of confusing the reader). Taking as given investment and financial policies, the

market value of the firm V satisfies that the after tax rate of return on equity equates the

investor rate of discount ρ:

ρ =d(1− τd)

V+V − eV

(1− τg)−δdV

V(1− τg), (1)

where V represents the rate of change of V with respect to time (age of the firm). Note

that increases in share values due to equity issuance are not taxable. Firm exit give rise

to negative capital losses that are tax deductible. The above no-arbitrage equation can be

re-arranged as (ρ

1− τg+ δd

)V =

1− τd1− τg

d− e+ V .

Denote m = ρ1−τg . Then, the solution to this first-order linear differential equation on V

gives the integral in (2). The problem of the firm in state (k,z) is then to choose investment

and financial policy to maximize:

V (k, z) ≡ max

∫ ∞0

e−(m+δd)t

{1− τd1− τg

d− e}dt (2)

subject to:

k = (1− τc)π(z, k)− d+ (1− ξ)ed ≥ 0, e ≥ 0, k0 given

Associate the present-value multipliers e−(m+δd)λt to the flow of funds constraint,

e−(m+δd)µet to the non-negativity constraint on equity issuance, and e−(m+δd)µdt to the non-

negativity on dividend distribution. Then, the FOC from the Maximum Principle imply:

λ =1− τd1− τg

+ µd (3)

(1− ξ)λ+ µe = 1 (4)

λ [m+ δd − (1− τc)π′(z, k)] = λ (5)

k = (1− τc)π(z, k)− d+ e(1− ξ) (6)

µd ≥ 0, µdtd ≥ 0, d ≥ 0 (7)

µe ≥ 0, µete ≥ 0, e ≥ 0 (8)

limt→∞

e−(m+δd)tλtkt = 0 (transversality) (9)

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Conditions (3) and (7), imply that the shadow value of funds λ ≥ 1−τd1−τg , with equality

if dividends are strictly positive. Conditions (4) and (8), imply that the shadow value of

funds λ ≤ 11−ξ , with equality if equity issuance is strictly positive. In sum, the shadow value

of funds satisfies λ ∈[

1−τd1−τg ,

11−ξ

].

2.2 Entry, optimal initial equity, and time to maturity

As in Hopenhayn and Rogerson (1993), firms pay a fixed cost ce to draw a productivity

z from an exogenous probability density ge. We assume that the firm decides the initial

amount of capital k0(z) after observing the productivity draw z. The value of entry is then

given by

V e =

∫ ∞0

V (k0(z), z)ge(z)dz = ce, (10)

where the second equality states that in a steady state equilibrium the value of entry should

be equal to the entry cost. The wage rate adjusts to ensure that this is the case. The mass

of firms entering the economy is determined by the labor market clearing condition:∫ ∞0

e−δdt∫ ∞

0

n(z, kt)g(k, z)dzdt = 1,where g satisfies (11)

0 = −∂k (s(k, z)g(k, z))− δdg(k, z) +Mge(z)Ik=k0(z),

where nt(z, k) and g(k, z) denote the optimal labor demand and the mass of firms in state

(k, z).

Consider a firm with productivity z that raises capital (equity) k0 when newly created.

The firm will accumulate capital until it reaches the optimal amount of capital k∗(z) (for

now we take k∗(z) as given, but in the next subsection of the paper we determine the optimal

scale of the firm). Once the firm reaches its optimal scale, it will start distributing dividends

until it dies. The age (T) at which the firm starts distributing dividends solves the following

equation:

(1− τc)∫ T

0

π(z, kt)dt+ k0 = k∗. (12)

The above equation defines an implicit function T (k0, z) characterizing the age when a firm

matures (starts distributing dividends) as a function of its net worth at entry (age 0). Since

an increase in initial capital k0 increases the profits accumulated by the firm over time, the

firm takes a shorter period to reach maturity. Formally, differentiating (12) with respect to

initial capital k0 yields

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dT

dk0

= −1 + (1− τc)

∫ T0π′(z, kt)

dktdk0dt

(1− τc)π(z, kT )< 0. (13)

In words, if initial capital k0 is greater, everything else held constant, the time to reach

maturity decreases.

We now focus on determining the optimal amount of initial equity. For a fixed value

of k0, we compute T from (12). Equations (3)- (7) imply that the shadow value of funds at

age T satisfies λ(T ) = 1−τd1−τg . Integrating (5) between 0 and T (k) gives

λ(0) =1− τd1− τg

e∫ T0 [(1−τc)π′(z,kt)−(m+δd)]dt (14)

The function inside the integral in (14) has a positive sign for all t < T , is equal to 0 at

T, and is decreasing on k0 (due to decreasing returns to capital accumulation). Moreover, T

is a decreasing function of k0 . As a result, it is easy to see that λ(0) is a decreasing function

of k0. The optimal value of initial equity is obtained by solving λ(0) = 1 + ξ.

The value of a firm with initial capital (equity) k0 satisfies

V (k0, z) =

∫ ∞T (k0,z)

1− τd1− τg

e−(m+δd)td∗(z)dt =1− τd1− τg

d∗(z)e−(m+δd)T (k0,z)

m+ δd(15)

where m = ρ1−τg is determined by the capital gains tax rate. Note that another way of solving

for the optimal amount of initial equity is

maxk0

V (k0, z)−1

1− ξk0, (16)

which implies

V ′(k0, z) =1− τd1− τg

d∗(z)e−(m+δd)T (k0,z)(−1)dT

dk0

=1

1− ξ(17)

Since V is a concave function of net worth, it follows that the solution for initial equity is

unique.

2.3 The life cycle of a firm

The previous discussion highlights that, as in Korinek and Stiglitz (2009), firms in our simple

model firms face three distinct phases during their life cycle: equity issuance phase, growth

phase, and dividend distribution phase.

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• Equity issuance phase. The first stage occurs when firms are created. Firms start

with zero net worth. In order to operate they need to raise equity at age 0 so that

e0 > 0. The Kuhn Tucker complementarity slackness condition (8) imply that µe0 = 0

so that (4) implies that the shadow value of assets at age 0 is given by λ0 = 11−ξ . The

non-negativity constraint on dividend distribution binds (µd0 > 0) so that firms do not

distribute dividends. The amount of initial equity raised is such that:

(1− τc)π′(z, k0) > m+ δd (18)

By equation (5), once the firm is set up and λ0 = 11−ξ , the next instant the value of

the multiplier is decreasing,i.e.limt→0+ λt <1

1−ξ . Otherwise, condition (18) implies

that limt→0+ λt >1

1−ξ , which violates the non-negativity of µet (see equation (4)). This

phase would fall within the so-called ‘traditional view’, where firms are using equity

issuance as the marginal source of financing.

• Growth phase. When firms start operation (immediately after age 0), the continuity

of λt together with (18) imply that the shadow value of net worth decreases since

(1 − τc)π′(z, kt) > m + δd for t > 0 in the right neighborhood of t = 0 (λt). Newly

created firms start operation and retain earnings in order to increase their net worth.

As net worth grows, the shadow value of funds decreases relaxing the non-negativity

constraint on dividends (its multiplier decreases).

• Dividend distribution phase. Firms reach the dividend distribution phase (matu-

rity) when the shadow value of funds reaches the value 1−τd1−τg . At this stage, the marginal

source of funds is retained earnings, and its marginal cost equals the marginal benefit of

distributing dividends. Growth ceases when firms reach a steady state with a constant

capital (k∗) and constant dividend distribution d∗ satisfying

(1− τc)π′(z, k∗) = m+ δd (19)

(1− τc)π(z, k∗) = d∗ (20)

2.4 Discussion on taxation and the life cycle of firms.

We now discuss, for a fixed wage rate, the effects of taxes on the life cycle of firms. To

analyze the effects of taxes on mature firms we use that in steady state m = r(1−τr)1−τg and

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r = ρ1−τr , (19)-(20) to obtain:

(1− τc)π′(z, k∗) =ρ

1− τg+ δd (21)

(1− τc)π(z, k∗) = d∗, (22)

Equations (21) and (22) determine the optimal level of capital (k∗) and dividends (d∗) by

mature firms. The value of a mature firm with productivity z is

V mature(z) =1− τd

ρ+ δd(1− τg)d∗. (23)

Using (15), m = ρ/(1−τg) implies that the value of an age-0 firm with productivity z satisfies

V new(z) =1− τd

ρ+ δd(1− τg)e−( ρ

1−τg+δd)T (k0,z) d∗ (24)

Below we use (21)-(24) to evaluate the impact of capital income taxation on mature

firms and on the market value of mature firms relative to that of age-0 firms.

Dividend taxation (τd) The tax rate on dividend distribution does not affect equations

(21) and (22). It is then immediate that dividend taxation has no impact on capital and

dividends paid by mature firms, a that result is consistent with the “new view” of the public

finance literature. When the firm is indifferent between using its marginal unit of funds as

dividend or investment, a change in the dividend tax rate has proportional effects in the

benefits and cost of investment. As a result, investment decisions and dividend payouts of

mature firms are unaffected by the dividend tax rate. However, the dividend tax reduces

the market value of mature firms (it changes proportionally with the term 1− τd, as shown

in (23)).

Paradoxically, the dividend tax rate affects capital accumulation when firms are not

paying dividends. This is because the lower value of the firm to shareholders reduces the

optimal amount of initial equity (see equation (17)), retarding the age at which firms reach

maturity. Intuitively, the firm can effectively diminish the taxes paid by reducing (initial)

equity issuance and by financing investment with retained earnings. The fact that the firm

reaches maturity at a later age, implies that dividend tax rate decreases the market value of

firms at entry more than at maturity (in (24) the increase in T caused by dividend taxation

further reduces the value of entry).

In sum, while dividend taxation does not distort the optimal scale and payouts of

mature firms, it distorts the initial scale of operation of firms, diminishing capital accumu-

lation along the life cycle and the age at which firms reach maturity. Moreover, in general

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equilibrium dividend taxation negatively affects the creation of businesses (entry).

Taxation of capital gains (τg) Taxation of capital gains (τg) reduces capital and dividend

distribution of mature firms since it increases the cost of equity financing ( ρ1−τg ). As a result,

the optimal amount of capital at maturity decreases (see equation (21) ) and so does the

dividends distributed (see equation (22)). The decrease in dividends imply a decrease in the

market value of mature firms.3

Relative to mature firms, the tax rate on capital gains τg has an additional effect on

the market value of new firms (see (24)): It increases the rate of discount of dividends

( ρ1−τg + δd). As a result, the taxation of capital gains incentivize firms to issue more equity

at entry so that the time to maturity diminishes and the firm value rises.4 Intuitively, by

raising more equity at entry, they avoid paying taxes on capital gains that would accrue

with the accumulation of internal funds. Hence, the capital gains tax encourages new firms

to finance investment with external funds. Note that this result is the opposite of what we

found for dividend taxation. Recall that, in order to minimize taxes on dividends, dividend

taxation encourages young firms to finance investment with internal funds.

Corporate income taxation (τc) Corporate income taxation reduces capital accumula-

tion and dividends paid by firms. Intuitively, corporate income taxation reduces the after

tax benefit to capital (see left hand side of equation (21) ) but without reducing the cost of

funds to the firm. This effect reduces the optimal size ( k∗ decreases) and distributions (d∗)

by mature firms (see equation (22)). Lower dividends imply a decrease in the market value

of mature firms (see equation (15)) which, in turn, decreases the optimal amount of initial

equity (equation (17)). Hence, firms start their life with a smaller scale. Moreover, the firm

grows at a slower pace since the corporate income tax reduces the fraction of earnings that

the firm accumulates during its growth face in the life cycle (see equation (12)). The time

to reach maturity may increase or not with corporate income taxation since there are two

opposite forces at work: While the firm grows more slowly, the optimal scale of the firm at

maturity is smaller. In our computational experiments, we shall find that the first effect is

stronger so that firms take a longer time to mature.

It is important to note that the decrease in d∗ associated with corporate income taxation

3Note that τg enters in the denominator of (23). This expression represents that the market value ofmature firms increase with τg because the tax code in our model ecomnomy allows for a tax credit associatedto the death of the firm. Quantitatively, this effect will likely have a small effect on the market value of firmsif the death rate is small. As a result, we should expect the market value of mature firms to move togetherwith d∗. This will always be the case if we assume that there are no tax credit associated to the capitallosses upon death of firms.

4The time to reach maturity diminishes because of a second effect: The optimal amount of capitaldiminishes with the capital gains tax rate.

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reduces proportionally the market value of firms at entry and at maturity. In addition,

for a fixed amount of initial equity, the corporate income tax makes it harder for firms

to accumulate retained earnings, retarding the age at which firms reach maturity. This

additional effect implies that corporate income taxation affects more negatively the market

value of firms at entry than at maturity. The asymmetric effect on market valuations at

entry and at maturity implies that the corporate income tax discourages entry, an effect

that will play an important role in the tax reform that we analyze in the next section of the

paper.

Quantitative illustration We parameterize the simple model in order to illustrate the

discussion on how various forms of taxing capital income affect the life cycle of firms.5 We

simulate in partial equilibrium (e.g. fixed wage rate) the life cycle of a firm in three different

scenarios: under the baseline parametrization, and after an increase of 5 percentage points

of each of the tax rates, maintaining everything else constant. Figure 1 plots the life cycle

profile of capital for the four cases considered. Consistent with our discussion above, we

find that firms start their life cycle with a lower amount of capital when they are subject

to dividend or corporate income taxation. The initial level of capital is slightly below under

dividend taxation than corporate income taxation. While the level of capital at maturity

is not affected by dividend taxation, it is negatively affected by corporate income taxation.

This is the key factor explaining why it takes the firm about one more year to reach maturity

under dividend taxation, despite the fact that the firm is able to accumulate capital faster

under dividend taxation than corporate income taxation. The latter explains why the age

profile of capital in the figure is steeper under dividend taxation than corporate taxation.

It is interesting to compare the effects of dividend taxation with those of capital gains

taxation. While dividend taxation does not distort capital accumulation of mature firms, it

has a large negative impact on the initial amount of equity at entry. In this way the firm

finance a larger portion of its investment over the life cycle with internal funds, diminishing

the present value of taxes paid on dividends. Capital gains taxes do precisely the opposite.

They encourage firms to finance a bigger fraction of their investment with external equity,

diminishing firm growth over the life cycle, and the present value of taxes paid on capital

gains. In terms of capital accumulation, the tradeoff is between distorting investments prior

to becoming mature (dividend taxation) versus distorting the optimal scale at maturity

(capital gains taxation). The corporate income tax distorts investments all over the life

cycle.

5We set the following parameters for the production function α = 0.3 × 0.85, η = 0.7 × 0.85. Thedepreciation of capital is fixed as δ = 0.05 and the rate of time preference is set so that the steady stateinterest rate is 4% (r = 0.04). The equity issuance cost is set to 0.10. The wage rate is fixed at 1. Taxes inbaseline are τc = 0.34, τd = 0.15, τg = 0.15 and τr = 0.25

13

Figure 1: Life Cycle of Firm

11.

52

2.5

3C

apita

l

0 2 4 6 8Years

Baseline Δ τc=5ppΔ τd=5pp Δ τg=5pp

Life cycle of three identical firms in equilibriums with different taxes. Blue is the

baseline: τc = 0.34, τd = 0.15, τg = 0.15 and τr = 0.25. Changes after an increase

of 5pp of each of the tax rates, maintaining everything else constant.

General equilibrium Changes in the taxation of capital income also have general equi-

librium effects that involve changes in the mass of entry of firms and the wage rate. Consider

the effects of corporate income taxes on entry. Since corporate income taxation makes it

hard for firms to retain earnings, it makes the impact of financial frictions on new firms

more severe that the one of dividend taxation. As a result, a switch from corporate income

to dividend taxation increases the value of the firm at entry more than the ones of mature

(or incumbent) firms. In general equilibrium, the free entry condition implies that the wage

should increase, leading incumbent firms to hire less workers. Equilibrium in the labor mar-

ket then requires an increase in the number of firms that is attained through higher entry

of firms. This mechanism points that, in general equilibrium, the corporate income tax acts

as a barrier to entry . We will quantitatively analyze these effects in the next section of the

paper.

3 The Stochastic Model Economy

We extend the simple model as follows. Time is still continuous6. Following the standard the-

ory of investment, we introduce adjustment costs in capital and uncertainty in productivity.

6 Achdou et al. (2017) advocate the use of continuous time models for analyzing heterogeneous agentmodels. We extend their methods to a model of firm dynamics with financial frictions.

14

Physical capital evolves according to

k = x− δk.

and the resource cost of investing x is given by x+ Ψx2

2k, where the second term reflects the

presence of adjustment costs in capital.

The productivity z of a firm follows a geometric Brownian Motion

dz = µzdt+ σzdW, (25)

where µ determines the drift and dW is a Wiener process. Since productivity follows a

geometric Brownian motion, large firms in our model follow Gibrat’s Law and growth rates

are independent of firm size. Empirical research, such as Hall (1987), suggests that Gibrat’s

law is a good approximation for firms that are not too small (see also Gabaix (2009)).

Similar specification of the productivity shocks has been widely used in the literature on

firm dynamics (see Atkeson and Kehoe (2005), Luttmer (2007), Da-Rocha et al. (2017),

among many others). Nonetheless, in Appendix C of the paper we consider the robustness

of our results to an alternative specification in which productivity follows an autoregressive

process.

The flow of a firm at time t in state (k, z) with investing expenditures x is given by

d− e(1− ξ) = (1− τc)π(k, z)− x−Ψkx2

2k, (26)

where

π(k, z) = maxn{y(k, n, z)− wn}.

The firm in state (k, z) solves the following optimal control problem:

v(k, z) = maxE0

∫ ∞0

{1− τd1− τg

d− e}e−(m+δd)tdt (27)

subject to:

dz = µzdt+ σzdW (28)

k = x− δk (29)

d− e(1− ξ) = (1− τc)π(k, z)− x−Ψkx2

2k+ τcδk. (30)

where m + δd is the rate at which the firm discount future payments to/from shareholders

when acting in their interest (see Appendix A).

15

Then, the Hamiltonian-Jacobi-Bellman equation of a firm satisfies:

(m+ δd)v(k, z) = max1− τd1− τg

d− e+ ∂kv(k, z)k + µzz∂zv(k, z) +(zσ)2

2∂zzv(k, z). (31)

We assume that upon entry firms draw the initial productivity z0 from a Pareto dis-

tribution:

ge(z0) =

ε1

zε+10

if z0 > 1

0 otherwise.(32)

The initial amount of equity raised by a firm that draws z solves the following problem:

k0(z0) = arg maxk0

{v(k0, z0)− 1

(1− ξ)k0} (33)

Then, the value of entry for a firm that draws z can be expressed as

ve(z0) = v(k0(z0), z0)− 1

(1− ξk0 (34)

In equilibrium the free entry condition requires

V e ≡∫ ∞

1

ve(z0)ge(z0)dz0 =

∫ ∞1

ve(z0)ε1

zε+10

≤ ce, (35)

with strict equality if there is positive entry.

The distribution of firms depends on firms investment and entry decisions. The measure

g of firms in state (k, z) satisfies:

0 = −∂k (s(k, z)g(k, z))− ∂z (µzzg(k, z)) +σ2z

2∂zzg(k, z)− δdg(k, z) +Mge(z)Ik=k0(z), (36)

where s = k = x− δk and M denotes the mass of firms entering the economy.

We assume that there is a representative household that owns the market portfolio

of firms. Households supply labor to firms, receive dividends, buy/sell shares of firms, and

trade bonds. Since households do not face uncertainty on their savings, in equilibrium there

is a no arbitrage condition (see Appendix A for its derivation) that equates the after-tax

return in bonds to the expected after-tax return in each firm.

The representative household maximizes discounted lifetime utility subject to the in-

16

tertemporal budget constraint

max{ct}

∫ ∞0

e−ρtu(ct)dt (37)

subject to: (38)∫ ∞0

e−r(1−τr)t(c− w − T ) = a0, (39)

a0 =

∫v(k, z)g(k, z)dkdz (40)

where a0 is the period-0 market value of all firms. In steady state equilibrium, rt(1− τr) = ρ

and ct = c ∀t. Note that given that firms can’t borrow, the assumption of a representative

consumer implies that bonds are in zero net supply b0 = 0 and households make zero interest

income.

Definition of steady state equilibrium Given a fiscal policy (τr, τc, τg, T ), a steady

state equilibrium is given by value functions for incumbent firms (v(k, z)), value of entry

V e, prices (w, r), firms policy functions on employment (n), investment in physical (x)

and financial policies (d,e) , initial equity k0, mass of entry M , measure of firms g(k, z),

consumption c and initial household assets a0 such that:

1. Given prices, the value function v(k, z) satisfy the HJB equation of the firm and firm

decisions (n, x, d, e) are optimal.

2. V e satisfy the free entry condition (35).

3. The government budget constraint is satisfied (all tax revenue is rebated back to con-

sumers as a lump sum transfer).

4. Household maximize utility taking as given government transfer, prices, and initial

wealth, which implies that steady state consumption is equal to permanent income:

c = ρa0 + w + T

5. Labor, bonds, and goods market clear∫n(k, z)g(k, z)dkdz = 1

c+ ceM +

∫ [x+ ψ

x2

k

]g(k, z)dkdz =

∫z1−α−γkαnγg(k, z)dkdz (41)

17

3.1 Firms’ Policies and its Life Cycle

The financial and investment policy of firms can be characterized using the FOC from the

HJB. The Lagrangean associated to the maximization problem in the HJB equation can be

written as:

L =1− τd1− τg

d− e+ ∂kv(k, z)(x− δk) + ∂zv(k, z)µz +(zσ)2

2∂zzv(k, z) + λdd+ λee+ ...

λk

{(1− τc)π(k, z)− x−Ψ

x2

2k− d+ (1− ξ)e

},

where λk represents the shadow price of capital (Tobin’s marginal q), λd and λe are the

multipliers on the non-negativity condition on dividends and equity issuance. The opti-

mal decisions on dividend distribution, equity issuance and investment should satisfy the

following conditions:

d :1− τd1− τg

+ λd − λk = 0 (42)

e : −1 + λe − λk(1− ξ) = 0 (43)

x : ∂kv(k, z)− λk[1 + Ψ

x

k

]= 0 (44)

KT : λdd = 0, λee = 0, λd, λe, d, e ≥ 0, (45)

where (45) are the complementarity slackness conditions from Kuhn-Tucker.

The shadow price of capital (λk) determines the financial policy of the firm. It is easy to

see that λk is bounded above by the cost of raising external funds ( 11−ξ ) and bounded below

by the after tax dividends received by the shareholder. In the former case the firm issues

equity and in the latter case it distributes dividends. Tax policy (e.g. when τd 6= τg) and

financial frictions create a wedge between these two bounds leading to an inaction region.

Indeed, when the shadow value of capital is in between these two bounds the firm does

not distribute dividends nor does it issue equity. In this case, the firm finances all of its

investment with retained earnings and all earnings are used to finance investment. Optimal

investment satisfy:

x =

[∂kv(k, z)

λk− 1

]k

Ψwhere λk ∈

[1− τd1− τg

,1

1− ξ

](46)

As in modern q theory, investment is an increasing function of the marginal value of

installed capital. Financial frictions imply that investment is also affected by the shadow

price of capital (λk). The rate of investment or disinvestment depends on the ratio between

the marginal value of capital and the shadow cost of funds. If this ratio is above 1, investment

18

rate is positive. If its below 1, the firm disinvests. For a fixed, marginal value of installed

capital,the concavity of the value function implies that investment is a decreasing function

of the shadow price of capital λk. The shadow cost of funds depends on the financial regime

of the firm. When equity issuance is the marginal source of funds, λk = 11−ξ . When the

firm distributes dividends, λk = 1−τd1−τg and the firm is indifferent between using the last unit

of earnings to finance dividend distribution or investment. When λk ∈(

1−τd1−τg ,

11−ξ

)firms do

not issue equity nor distribute dividends. In this case, all available funds are used to finance

investment.

Figure 2: Policy functions for different Z

A: Investment

0 10 20 30 40 50 60Assets

-90

-80

-70

-60

-50

-40

-30

-20

-10

0

10

Inve

stm

ent

Investment Policy

B: Net Payout (Dividends-Equity)

0 10 20 30 40 50 60Assets

-20

-10

0

10

20

30

40

50

60

70

80

Div

iden

ds -

Equi

ty Is

s.

Payout Policy

Investment and payout policy (y-axis) by level of assets (x-axis) for different levels of productivity. Each parallel line

corresponds to a level of productivity.

Figure 2 plots the investment and financial policy as a function of the capital installed

by firms in our calibrated model economy. Each line in the figures correspond to a firm

with different a level of productivity. It is instructive to consider the life cycle of a firm that

enters the economy with a fixed productivity level z . If the initial level of installed capital

is low enough, optimal investment is an inverted U-shaped function of capital (see Panel A).

An increase in installed capital has two opposite effects on optimal investment (see equation

(46)). On the one hand, the marginal value of capital to the firm decreases (∂kv(k, z) ↓),thereby pushing investment down. On the other hand, the presence of adjustment costs

imply that the cost of investment decreases with the level of installed capital. This effect

explains why the optimal level of investment initially rises with capital (as reflected by the

positive effect that the term k outside the straight bracket in (46) has on x). The first force

dominates at low levels of capital and the second force at high levels of capital, explaining

19

the inverted U-shaped of investment as a function of capital. Note that a (young) firm with

low level of capital finance investment by issuing equity (see Panel B). As capital increases,

the firm makes more profits and can finance a bigger fraction of investment with retained

earnings. The firm fully finance investment with retained earnings when installed capital

becomes sufficiently large, thereby avoiding external financing costs. Once firms finance

all investment with internal funds, the investment policy becomes an increasing function

of installed capital (and earnings) until the firm reaches its optimal level of capital. This

occurs when the level of capital is such that the shadow price of capital equates the after-tax

value of dividend distribution to the shareholders. At this point, the firms starts distributing

dividends. Higher values of installed capital then lead to higher dividend distribution and

to lower investment. When installed capital is large enough, investment becomes negative

as the firm finds it optimally to disinvest in order to finance dividend distribution.

In the presence of uncertainty, shocks to firms productivity may change their financial

and investment policies. A firm that is increasing its capital and issuing equity, may stop

doing so if productivity decreases. When productivity decreases by a large amount, the

firm may even start distributing dividends and disinvesting. Conversely, an increase in

productivity may move back the firm to the equity issuance and investment regime.

3.2 Quantitative Analysis

3.2.1 Calibration

The calibration targets aggregate and firm level data from the US economy. In principle,

our goal is to target all US businesses that pay corporate income taxes. The calibration re-

quires targeting “dynamic moments” from US firms, such as average firm growth, volatility

and autocorrelation of investment rates over time. We follow Gourio and Miao (2010) in

using Compustat data to pin down these calibration targets. Nonetheless, we should keep

in mind that the Compustat data covers publicly traded firms that only represent a small

subset of US corporations. We thus also target cross-sectional data on the size distribution

of businesses from US Census Bureau. Now, the universe of US businesses include private

pass-through businesses that are not subject to the US corporate income tax (S corpora-

tions, partnerships).7 Since most of these businesses tend to be small, as a compromise we

target data on the size distribution of businesses that includes businesses with more than 50

employees. We divide the set of parameters to be calibrated in two groups.

Parameters assigned without solving the model. We use data from the Internal

Revenue Service for the year 2015 to set the tax parameters. We set the corporate income tax

7Developing a theory of organizational choice (pass through entities versus C corporations) is outsidethe scope of the current paper. See Dyrda and Pugsley (2018) for a theory of organizational choice.

20

rate to 34% (τc = 0.34)8 We set the capital gains tax rate to 0.15 (τg = 0.15), the dividend tax

rate to 0.15 (τd = 0.15), and the interest income tax rate to 0.25 (τr = 0.25) to the marginal

Federal taxes faced by a married couple with the average household income in the US. We

assume that households discount future utility at an annual rate of 0.0375 (ρ = 0.0375) so

that the (before tax) steady state return on capital is 5%, consistent with the estimates of

the return on capital by Cooley and Prescott (1995). The parameters on the production

function are set to standard values in the literature: the profit share is set to 0.15, with 70%

of the remaining share going to labor and 30% to capital (α = 0.85∗0.3, η = 0.85∗0.7), as in

Midrigan and Xu (2014). The depreciation rate of capital is set at 0.05 per year (δk = 0.05).

Based on data from US Census Bureau’s Business Dynamic Statistics (BDS), the average

annual exit rate of firms with more than 50 employees is 4.6% so we set δd = 0.046. Using

data from Thomson Reuter’s Securities Data Company (SDC) Platinum, we find that during

the period 1995-2015 the total costs of equity issuance as a percentage of proceeds is about

7%9. This is computed following closely the procedure of Lee et al. (1996) for IPO firms. It

is somewhat smaller than the ones reported by Hennessy and Whited (2007), who estimated

equity issuance cost in the range of 8.3% to 10.1%. We thus set the cost of raising external

fund to 0.07 (ξ = 0.07). Nonetheless, we assume that firms raising their initial capital at

entry face a higher equity issuance cost ξe. This parameter will be determined later by

simulating the model economy. As we shall see our calibration requires that ξe > 0.07 in

order to match the equity issuance by incumbent firms.

Parameters assigned by solving the model. It remains to assign the parameters

driving the stochastic process on productivity (µz, σz), the parameter Ψ driving adjustments

costs, the productivity distribution of firms that enter the economy and their cost of raising

external capital. We assume that firms that enter draw the initial productivity from a

Pareto distribution with tail parameter ηp and a location parameter 1 (the lowest possible

productivity is one). We normalize the wage rate to 1 and set the fixed cost of entry equal

to the value of entry.

Targeted moments. Although the endogenous equilibrium outcomes of interest will

be jointly determined by all of these parameters, each of these parameters is intuitively

connected with a particular moment of interest. The parameter µz will be closely connected

with firm growth and σz with the variance of investment. The parameter Ψ is closely

related to the correlation of investment rates across two consecutive years and the parameter

determining the Pareto tail with the size distribution of businesses. Finally, the cost of raising

initial equity is closely connected to the amount of external finance by incumbent firms. With

8The progressive rate structure of the Federal corporate tax in the US is designed such that it producesa flat 34% tax rate on incomes from $335,000 to $10,000,000, gradually increasing to a flat rate of 35% onincomes above.

9See Appendix B.2 for more details on the data and computation.

21

these connection in mind we target the following statistics:

1. An average annual employment growth of 2.1%.

2. The volatility of the investment rate (x/k) among firms of 0.059.

3. The autocorrelation of investment rates between two consecutive years of 0.57.

4. The ratio of equity issuance by incumbent firms to investment of 12.6%.

5. The size distribution of businesses, computed using data from BDS and reported in

Table 2.

The first 4 targets were computed using Compustat data from over the period 1995-

2015.10 For the reasons previously discussed, in computing the size distribution of businesses

we abstracted from small businesses in the BDS and focused on businesses with more that

50 employees. Tables 1 and 2 show the parameter values and the calibration results.

Table 1: Calibration Baseline Economy

Parameter Description Valueψ Capital adjustment cost 0.09µ Productivity drift -0.00325σ Volatility of prod. shock 0.15ξe Financing cost at entry 0.30ηp Distribution of businesses 1

Parameter values and discussion. The model accounts well for the targeted mo-

ments. We now discuss how some key parameters help attaining the calibration targets.

The baseline economy matches the average employment growth of 2.1 percent in the data.

Recall that productivity in our model economy follows a geometric Brownian Motion with a

drift given by µ = µz + σ2z

211. Hence, the variance of shocks is a force driving firm growth.12

We find that the model economy accounts for the 2.1% in average employment growth with

µz = −0.00325. To measure the volatility of the investment rate and its autocorrelation

over time in our baseline economy, we first solve the model to compute the stationary dis-

tribution of firms. Then, we draw firms from this distribution and simulate them over the

year to compute annual investment rates. The annual volatility of the investment rate in

10See Appendix B.1 for more information about the data and variable construction.11This follows from Ito’s lemma, and the specification of the process of productivity growth in our model,

i.e. dlnz = µzdt+ σzdW12 Moreover, the distribution of productivity at entry is such that most businesses in our baseline economy

start their life with a low productivity level, not far from the minimum value of 1 which represents a lowbarrier on z.

22

Table 2: Calibration Results

Data ModelTarget

Avg. employment growth 0.02 0.02Volatility investment rate 0.059 0.054Autocorrelation invest. rate 0.57 0.59Eq. issuance incumbents/investment 0.13 0.13

Size Distribution of BusinessesNo. of Employees Fraction Data Fraction Model[50, 99) 0.53 0.50[100, 249) 0.29 0.22[250, 499) 0.089 0.13[500, 999) 0.0429 0.07[1000, 2499) 0.0265 0.047[2500, 4999) 0.0099 0.018[5000,∞) 0.0115 0.0057

Targeted moments in the data, and their respective counterpart in the model. Data comes from Com-

pustat, and BDS for the size distribution of businesses.

the baseline economy is 0.054, which is close to the value of 0.059 in the data. Matching

this target requires a significant variance in productivity since σz = 0.1513. The parame-

ter ψ = 0.07 is set to match the autocorrelation of annual investment rates over two years

across the stationary distribution of firms. This parameter is between the 0.049 estimated

by Cooper and Haltiwanger (2006) and the 1.08 value obtained by Gourio and Miao (2010).

The size distribution of businesses in the baseline economy is determined by the distribution

of businesses at entry and by the stochastic growth in productivity over the life cycle of

firms. The model accounts reasonably well for the size distribution of businesses, although

the match is not perfect. The model implies that 50 percent of business have less than 100

workers, and 22 percent of businesses employed between 100 workers and 250 workers. The

corresponding fractions in the data are 53 precent and 29 percent. The fraction of businesses

with more than 5000 employees are about 0.6 percent in the model economy and 1% in the

data14.

A crucial parameter in our model economy is given by the cost of external financing.

As in Korinek and Stiglitz (2009), financial frictions matter for the different financial regimes

13Nonetheless, recall that z in the production function is raised to the power of 0.15 so that the varianceof TFP is much smaller than the one in z. For instance, Gourio and Miao (2010) estimate a variance in TFPof 0.2, though in their model TFP follows an autoregressive process with persistence of about 0.8

14In the data, most large firms are multi-establishment, a fact that our model cannot account for. Thisis the main reason our model underpredicts mass in largest size category.

23

that firms go over their life cycle15. In particular, we want our model economy to be consistent

with data on firm growth, investment rates, and the fraction of investment financed raising

capital on the equity market. Recall, that the cost of external finance was set exogenously

at 7 percent using data from SDC Platinum. The model economy matches the 13 percent

target for the fraction of investment financed by equity issuance among incumbent firms.

To match this statistic the model requires that firms that entry face substantial financial

frictions. The baseline economy assumes that when firms enter the economy face equity

issuance costs of 0.30. Lower values of equity issuance costs at entry, will imply that firms

will raise a substantial amount of equity when they enter in order to invest a large amount

and avoid on expected adjustments costs in capital as they grow (in expectations) over their

life cycle. While we do not have data on the cost of raising external funds when firms

are created, we find that the cost of raising external funds in initial public offerings in the

SDC data is about 12%. Presumably, the cost of raising external funds when businesses

are actually created should be much larger. Moreover, our model assumes that firms learn

their productivity before making the initial investment in capital. Firms in our model would

invest less when they enter if they face some uncertainty on their initial productivity and

learn it over time. Hence, our calibrated equity issuance cost at entry may be capturing the

effects of information frictions that our model abstracts from.

Other non-targeted moments. The aggregate investment rate (x/k) in the model

economy is 0.096 somewhat above the 0.086 value from the National Income Accounts.

The model economy overstates the ratio of aggregate dividends to aggregate earnings in

Compustat (0.45 versus 0.098). This also happens in the model by Gourio and Miao (2010).

Perhaps, this should not be surprising since both model economies abstract from share

repurchases which is another way of dividend distribution. The model does a decent job

in matching the ratio of aggregate equity issuance to aggregate investment in the data

(0.15 versus 0.19). Moreover, the share of equity issuance by entrants relative to aggregate

investment is 0.037 in the data and 0.067 in the model.16

In Figure 3, we plot age profile of employment growth by firms 17 in the model and

the data. Although being an untargeted moment, the model captures quite well the sharp

decline in employment growth as firms age. In our model economy young firms are small

15Gourio and Miao (2010)’s model abstracts from financial frictions and life cycle. Firms in their modelgo through different financial regimes because of the differential tax treatment on dividends and capital gainsduring the year 2003.

16To measure the share of equity issuance by new entrants and by incumbents in Compustat, we sum upthe equity issuance of all firms that report doing an IPO in that same year on one side, and the rest of thefirms operating in that year on the other, and divide both by the sum of investment in capital expendituresof all firms.

17Unfortunately, age is not a variable available in Compustat, so we construct a proxy with the availabledata, and define age as years since their IPO.

24

Table 3: Non-targeted Moments

Variable Data ModelInvestment rate 0.086 0.096Dividends/Earnings 0.098 0.45Agg. eq. issuance/ agg. investment 0.15 0.19Eq issuance entrants/agg. investment 0.037 0.067

Non-targeted moments in the data, and their respective counterpart in the

model. Data moments from Compustat.

and constrained, so they grow fast at the beginning. As they age and accumulate internal

funds, they are likely to become less constrained and progressively reach their optimal size.

As a result, the age-profile of employment growth of firm is expected to decrease with age.

The fact that the baseline economy matches reasonably well the decline in the growth rate

of employment with age suggests that the model is not exaggerating the impact of financial

frictions on firm growth.

Figure 3: Employment growth by age in the model and the data.

0 5 10 15 20 25 30Age

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

Ave

rage

Em

ploy

men

t Gro

wth

Employment Growth by Age

ModelData

Average employment growth by age. Data from Compustat, where age is computed

in the as years since IPO (see Appendix B.1).

3.3 Aggregate effects of reforming the taxation of capital income.

We now consider the long run effects of a tax reform that eliminates the taxation of corporate

income while keeping constant the tax revenue collected on capital income. This is done by

25

finding the common tax rate (τ) on all forms of capital income (dividends τd, interest income

τr, and capital gains τg) that collects the same tax revenue as in the baseline economy. The

purpose of the proposed policy reform is twofold. Firstly, by equating the three tax rates we

would be treating symmetrically all capital income from the household perspective. Secondly,

by eliminating the corporate tax, we allow financially constrained firms to accumulate profits

and to reach maturity (the dividend distribution stage) faster (in expectations).

We emphasize that the key insights from our simple model apply to the current stochas-

tic model. Financial frictions imply that firms start their life constrained. For fixed produc-

tivity, firms build internal equity over time, becoming less constrained and eventually will

start distributing dividends. Stochastic shocks imply that firms distributing dividends might

become liquidity constrained again if their productivity grows sufficiently over time, so that

the “life cycle process” is initiated again. By reducing the corporate tax and increasing the

dividend tax, our proposed tax reforms intends to shift the tax burden from liquidity con-

strained firms (with high marginal valuation of capital) to firms distributing dividends (with

low marginal valuation of capital). However, the effects of the reform are more involved

than it seems at first sight. This is because firms react to the higher dividend taxes by

diminishing initial equity, rising the likelihood that firms become liquidity constrained, and

(partly) reversing the gains pursued with the elimination of corporate income taxation (see

Section 2.4).18 To minimize these effects, our proposed tax reform involves raising capital

gains taxes together with dividend taxes. The rise in capital gains taxes encourages firms

to issue more equity in order to minimize taxes paid on capital gains, (partly) undoing the

distortions of dividend taxation on initial equity decisions (see discussion in Section 2.4).

To check for potential non-linearities in our results, we also consider a tax reform that

reduces the tax rate on corporate income to a half relative to the baseline economy (τc is

reduced from 0.34 to 0.17), again keeping aggregate revenue from capital income taxation

constant. To isolate the role of capital gains taxation from dividend taxation, we consider a

tax reform in which the corporate income tax is set at 0.17, but we only increase dividend

taxes to clear the government budget, while maintaining the other tax rates equal to their

baseline value.

Tax reform 1: Eliminate corporate income taxes

The results are shown on Table 4. We find that the elimination of the corporate income taxes

in the baseline economy (τc = 0.34) should be accompanied by an increase in capital income

taxes to 0.39 to keep government revenue constant (recall that in the baseline economy the

dividend and capital gains tax was set to 0.15 and the interest income tax was set to 0.25).

This revenue neutral tax reform leads to an increase in aggregate output of 13.6%, which

18 By financing a larger fraction of investments with internal funds, they reduce the cost of capital.

26

Table 4: Effects of Tax Reforms

Panel A: Aggregate Effects.

Output Capital TFP Mass Entry Wage Revenue Neutral Tax

1.- τc = 0 13.6 35.2 5.2 39.3 13.6 τd = τg = τr = 0.392.- τc = 0.17 8.1 20.1 3.1 22.7 8.1 τd = τg = τr = 0.283.- τc = 0.17 0.34 15.5 -3.3 -17.3 0.34 τd = 0.41, τg = 0.15, τr = 0.25

Panel B: Effects on Initial Size and Firm Value

Average Average Value Average Value Revenue Neutralk0 Entrants Incumbents Tax

1.- τc = 0 5.1 1.1 -1.4 τd = τg = τr = 0.392.- τc = 0.17 1.3 0.3 -1.0 τd = τg = τr = 0.283.- τc = 0.17 -10.2 -2.2 4.8 τd = 0.41, τg = 0.15, τr = 0.25

Percent changes from the baseline. Value of entrants is gross of initial equity payment. In each experiment, we decrease cor-

porate tax, but change other taxes such that the government revenue is constant. First row corresponds to Tax Reform 1

(τc = 0, τd = τg = τr = 0.39). Second row corresponds to Tax Reform 2 (τc = 0.17, τd = τg = τr = 0.28). The third row

corresponds to Tax Reform 3 (τc = 0.17, τd = 0.41, τg = 0.15, τr = 0.25).

is accompanied by a large increase in the aggregate capital stock (35.2%), in the number of

firms (39.3%), and in aggregate TFP (5.2%). Note that the fact that aggregate capital and

output rise less than the number of firms, indicates that both capital per firm and output

per firm decrease. The large response of firm entry to the tax reform is crucial for the large

increase in aggregate output and aggregate TFP.

It is interesting that the tax reform rises firm entry and wages at the same time.

The tax reform benefits constrained firms (firms with low capital relative to productivity),

regardless of their absolute level of productivity. Note that in Melitz (2003), the trade reform

benefits mostly large firms who are the ones that export due to the presence of fixed costs

of exporting. This asymmetric effect leads to a labor reallocation from small to large firms,

raising the equilibrium wage rate and reducing the number of firms. On the contrary, in our

model economy the tax reform affects symmetrically firms with different productivity levels

(z) at entry and leads to a large increase in entry.

Crucially for our results, the tax reform increases more the expected value of entry

(for all firms) than the value of incumbent firms, which leads to a reallocation of resources

from mature to younger firms, and hence to an increase in entry and in the equilibrium

wage rate. In understanding this result note that corporate income taxation has asymmetric

effects across firms depending on their financial regime. The elimination of corporate income

27

taxation allows financially constrained firms to retain a larger fraction of their earnings

and increase their investments. The ability to retain earnings is particularly relevant for

young firms, which are more likely to be constrained than the average incumbent firm in the

economy. Since the value of entry is determined by the average value of age-0 firms, this

observation explains why we find that, keeping fixed the wage of the baseline economy, the

value of the average firm entering the economy increases more than that of incumbent firms

(67% versus 62%) when corporate income taxation is eliminated. In general equilibrium,

the increase in the value of entry requires the wage rate to rise by about 13.6% in order to

restore the free entry condition. As a result, the value of entry does not change (it is fixed

by the cost of entry) but the value of incumbent firms decreases by 1.4%. The rise in wages

reduces labor demand by incumbent firms. Labor market clearing requires a larger mass of

firm entry, which rises by about 39.3%. Larger firm entry together with a reallocation of

resources to financially constraint firms explain the large increase in aggregate TFP.

In sum, we find that in general equilibrium corporate income taxation raises the market

value of incumbent firms relative to entrants, depressing the equilibrium wage rate and

business entry, shifting resources from young to mature businesses and reducing aggregate

output and TFP.

Tax reform 2: τc = 0.17 increasing all other capital income taxes

The corporate income tax rate is set as τc = 0.17 while all other capital income taxes are

set to 0.28 (τg = τd = τr = 0.28). We find that output increases by 8.1% and entry increases

by 23% (see Table 4). The results are somewhat more than a half the ones obtained when

the corporate income taxation was eliminated (13.6% increase in output and 39% increase in

entry). Hence, the effects on output and entry of reducing the taxation of corporate income

are non-linear but not too far from linearity.

Tax reform 3: τc = 0.17 increasing only dividend tax

The corporate income tax rate is set as τc = 0.17, and we increase τd = 0.41 so that the

reform is revenue neutral. Capital gains tax and income tax are kept fixed at their value

in the baseline economy. The results in Table 4 show that the output gain diminishes

dramatically relatively to the previous reform (0.34% versus 8.7%). Hence, the output gains

of equating the tax rates on capital gains and dividends are substantial. Why is this the

case? When τg is substantially below τd, firms have strong incentives to accumulate capital

internally (see discussion in Section 2.4). As a result, firms enter the economy with a small

size. The average initial equity is reduced by 10% relative to the baseline economy (while in

tax reform 2 is slightly higher than in the baseline economy). Firms take more time to grow

28

which reduces the value of entrants. As a result, relative to the baseline economy entry is

reduced by 17.3%. The fact that aggregate capital rises by 15.5% while the number of firm

decreases implies that the average firm is much bigger than in the baseline economy. In sum,

higher dividend taxes act as a financial frictions that hurt entry and make incumbents firms

much larger.

3.3.1 Taxation and the life cycle of firms

It is interesting to compare the average life cycle behavior of firms across the model economies.

Panel A of Figure 4 shows the average equity to investment ratio for the baseline economy

and the economies with the Tax Reforms 2 and 3. When the capital gains tax is smaller

than the dividend tax (Tax Reform 3), firms are much more reluctant to finance investment

with equity issuance. Moreover, as shown in Panel B of the same Figure, firms distribute

much less dividends when young in Tax Reform 3 because they are (slowly) building internal

equity. Nonetheless, when firms mature there are no differences in the dividends to earnings

ratio under the Tax Reforms 2 and 3. Mature firms in the baseline economy distribute a

lower fraction of their earnings because they are paying higher corporate taxes than in the

other two economies. Panel C of Figure 4 shows that the mean employment growth rate

of firms is much higher under Tax Reform 3. Again, when capital gains taxes are lower

than dividend taxes, firms start small and grow fast by retarding dividend payments and

accumulating internal equity. Since firms discount future payouts at a low rate when capital

gains taxes are low, they have a strong incentive to grow over their life cycle. Even though

the average firm size at entry is the smallest under Tax Reform 3, the average size late in

the life cycle is the largest across all economies. The large dispersion in business size over

the life cycle and the low entry under Tax Reform 3 explain why this economy features the

lowest TFP among all the economies considered.

4 Conclusions

In this paper, we use a model of firm dynamics with endogenous entry to analyze the impact

of different forms of taxing capital income on investment over the life cycle of firms and

on firm entry. We use the calibrated model economy to quantitatively assess the effects of

a reform that eliminates the taxation of corporate income while keeping constant the tax

revenue collected on capital. This is done by finding the common tax rate (τ) on all forms

of capital income (dividends τd, interest income τr, and capital gains τg) that collects the

same tax revenue as in the baseline economy. The purpose of the proposed policy reform is

twofold. Firstly, by equating the three tax rates we would be treating symmetrically all forms

of capital income from the household perspective. Secondly, by eliminating the corporate

29

Figure 4: Life Cycle of Firms

A: Equity to Investment by Age

0 5 10 15 20 25 30 35 40 45 50Age

0

0.05

0.1

0.15

0.2

0.25

0.3

Ave

rage

Equ

ity/N

et In

vest

men

t

Equity/Net Investment by Age

BaselineOnly d

d= g = r

B: Dividends to Earnings by Age

0 5 10 15 20 25 30 35 40 45 50Age

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Ave

rage

Div

iden

ds/E

arni

ngs

Dividends/Earnings by Age

BaselineOnly d

d= g = r

C: Employment Growth by Age

0 5 10 15 20 25 30 35 40 45 50Age

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

Ave

rage

Em

ploy

men

t Gro

wth

Employment Growth by Age

BaselineOnly d

d= g = r

D: Average Capital by Age

0 5 10 15 20 25 30 35 40 45 50Age

0

0.5

1

1.5

2

2.5

3

Cap

ital

Capital by Age

BaselineOnly d

d= g = r

Average age profiles for equity to investment, dividends to earnings, employment growth and capital. Blue solid line (Baseline)

corresponds to the baseline calibration. Dotted yellow line (τd = τg = τr) corresponds to Tax Reform 2, i.e. τc = 0.17, and

τd = τg = τr = 0.28 to keep the governement budget constraint balanced. Starred orange line (Only τd) corresponds to Tax

Reform 3, i.e. τc = 0.17, and τd = 0.41 to keep the governement budget constraint balanced, while the other taxes are set to

their baseline values (τg = 0.15, τr = 0.25).

30

tax, we allow financially constrained firms to accumulate profits and to reach maturity (the

dividend distribution stage) faster. We find that the this revenue neutral tax reform leads

to an increase in aggregate output of 13.6%, which is accompanied by a large increase in the

aggregate capital stock (35%) and in the number of firms (39.3%). Note that the fact that

aggregate capital and output rise less than the number of firms indicates that the average

size of the firm is smaller after the tax reform. Hence, the large response of firm entry to

the tax reform drives the large increase in aggregate output and capital.

At the heart of our results is that the tax reform increases more the expected value of

entry than the value of incumbent firms, leading to a reallocation of resources from mature

to younger firms that operates through an increase in entry and in the equilibrium wage

rate. The elimination of corporate income taxation allows financially constrained firms to

retain a larger fraction of their earnings and increase their investments. The ability to retain

earnings is particularly relevant for young firms, which are more likely to be constrained

than the average incumbent firm in the economy. Since the value of entry is determined

by the average value of age-0 firms, we find that the value of the average firm entering the

economy increases more than that of incumbent firms when corporate inome taxation is

eliminated. In general equilibrium, the increase in the value of entry requires the wage rate

to rise, which reduces labor demand by incumbent firms. Labor market clearing requires

a larger mass of firm entry. Larger firm entry together with a reallocation of resources to

financially constraint firms lead to an increase in aggregate TFP of 5.2%.

Our paper abstracts from many effects of corporate income taxation. In particular,

the corporate income is likely to affect the organizational form of firms, the incentives of

firms to borrow and to invest in intangibles capital. While these issues are out of the scope

of the current paper, they are important for having a complete assessment of the impact of

corporate income taxation.

31

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33

Appendix

Appendix A. Asset Pricing

We derive some useful results on asset prices by considering a discrete time version of the

model with δd = 019. Consider a small time interval ∆. In equilibrium the following no

arbitrage condition must hold:

∆Rt =1

PtEt

[(1− τd)dt+∆∆ + (1− τg)(Pt+∆ − et+∆

1

(1− ξ)∆− Pt)

], (47)

where R = r(1− τr) denote the returns on bonds.

Dividing by ∆ in both sides yields:

Rt =1

PtEt

[(1− τd)dt+∆ − (1− τg)et+∆ + (1− τg)

Pt+∆ − Pt∆

](48)

Taking the limit as ∆→ 0, yields expression (1) in the text.

To obtain the HJB equation satisfied by the firm value function, use (47) to solve for

Pt:

Pt =Et

{[1−τd1−τg dt+∆ − et+∆

]∆ + Pt+∆

}1 + ∆Rt

1−τg

(49)

Define the cum-dividend value of equity net of taxation on dividends and capital gains

as: (for every t):

Vt =

[1− τd1− τg

dt − et]

∆ + Pt (50)

Combining (50) and (49) yields:

Vt =

[1− τd1− τg

dt − et]

∆ + Et

(Vt+∆

1 + ∆Rt1−τg

). (51)

The date-0 value of the firm is obtained as follows:

V0 = E0

∞∑t=0

[1− τd1− τg

dt − et]

∆1

Πtj=0

(1 +

∆Rj1−τg

) , (52)

19The analysis in Appendix A builds on Gourio and Miao (2010).

34

which taking the limit ∆→ 0 yields:

V0 = E0

∫ ∞0

[1− τd1− τg

dt − et]e−

∫ t0 Rsds

1−τg , (53)

which gives the objective function in the problem of the firm stated in the text.20

To derive the HJB equation, re-arrange equation ?? to get

Rt∆Vt = [(1− τd)dt − (1− τg)et] ∆

(1 +

Rt∆

1− τg

)+ (1− τg)Et(Vt+∆ − Vt) (54)

Dividing by ∆ and taking the limit ∆→ 0 gives

RtVt = (1− τd)dt − (1− τg)et + (1− τg)Et(dVt) (55)

Applying Ito’s Lema, E(dV ) = ∂V∂t

+ ∂V∂zµz + 1

2∂2V∂z2

(σzz)2

Hence,

RtVt = (1− τd)dt − (1− τg)et + (1− τg){∂V

∂t+∂V

∂zµz +

1

2

∂2V

∂z2(σzz)2

}(56)

Dividing both sides of the above equation by 1− τg yields:

Rt

1− τgVt =

1− τd1− τg

dt − et +∂v

∂t+∂v

∂zµz +

1

2

∂2v

∂z2(σzz)2, (57)

which coincides with the HJB equation in the paper.

Appendix B. Data Variables

Appendix B.1. COMPUSTAT North America

We use data from COMPUSTAT North America obtained via WRDS. We use an unbalanced

panel of firms from 1995-2015. We exclude all Canadian and foreign firms. We also exclude

firms whose industry classification is in utilities (SIC codes between 4900 and 4949) or

the financial sector (SIC code between 6000 and 6999), following the literature21. We also

exclude observations reporting a value of acquisitions to assets larget than 5%, since these

firms might behave differently. We finally exclude firms reporting negative employment,

sales, wages or investment. All dollar values are in million dollars (1999 real terms, deflated

20The discount rate in the paper is denoted by m = R1−τg = r(1−τr

1−τg . When exogenous death of the firm is

allowed, firms discount future payout at a rate m+ δd, where δd is the death rate. The value of the firm inthe deterministic problem is just a special case of the stochastic case.

21These companies are usually excluded since they face additional regulations and hence might havedifferent payout behavior, and their dividend patterns are quite different from other companies.

35

using the GDP deflator from the U.S. Bureau of Economic Analysis22), and all firm-level

measures are winsorized at the 1st and 99th percentile. The raw variables we are going to

use are the following:

• Dividends. Total amount of dividends, other than stock dividends, declared on all

equity capital of the company, based on the current year’s net income (DVT item).

We restrict the analysis to those reporting DVT greater or equal to 0.

• Equity Issuance. Funds received from issuance of common and preferred stock

(SSTK item). We restrict the analysis to those reporting SSTK greater or equal to 0.

• Capital. It represents the cost, less accumulated depreciation, of tangible fixed prop-

erty used in the production of revenue, which is a component of total assets (PPENT

item).

• Age. Computed as current year minus year of their IPO (IPODATE item)23.

• Employees. Number of company workers as reported to shareholders. This is reported

by some firms as an average number of employees and by some as the number of

employees at year-end (EMP item).

• Earnings. Measured as Operating Income Before Depreciation (OIBDP item).

Table 5 presents the summary statistics of the variables over the period.

Table 5: Summary Statistics Compustat

Variable Mean Median Std. Dev. NDividends 44.43 0 195.71 104381Equity Issuance 21.81 .68 68.71 103368Capital 863.10 23.52 3056.73 105516Age 7.10 6 6.65 113580Employment 8.36 .65 24.07 96425Earnings 455.90 10.94 2429.87 104864Source: Compustat North America

We construct the variables used in the calibration as follows. The calibration targets

are the average of these variables over the sample.

• Employment growth. Computed asempi,t−empi,t−1

(empi,t+empi,t−1)/2.

22Accesed at https://www.bea.gov/iTable/iTable.cfm?ReqID=9step=1reqid=9step=1isuri=123Though an imperfect measure of firms’ age, it is the only one available in Compustat database. This

variable presents a high correlation with actual age, so that can be used as a proxy.

36

• Aggregate Investment rate. Computed from NIPA table 1.1.5 and FAT table 1.1.

• Aggregate Dividends to Earnings. Measured as the sum of dividends of all firms

alive in one period, divided by the sum their earnings (OIBDP).

• Aggregate Equity to Investment. Measured as the sum of equity issuance of all

firms alive in one period, divided by the sum their earnings (OIBDP). Equity issuance

of incumbents is the sum of equity issuance of all firms alive in one period that are not

doing an IPO, and equity issuance of entrants the sum of equity issuance reporting to

do an IPO in the period.

• Aggregate Employment Growth by Age. Computed as the sum of all labor of

firms of age j at time t (sum empj,t) for all ages and years in our data. Then, compute

the growth rates by age as(sum empj+1,t+1−sum empj,t)

((sum empj+1,t+1+sum empj,t)/2), and averaging by age j across

all years t in our sample.

Appendix B.2. SDC Global New Issues database

We use the Thompson’s Securities Data Corporation (SDC) Global New Issues database. We

only use the subset of observations from SDC that we can match to the previous Compustat

observations through their CUSIP. We keep only those observations trading in main stocks

markets: NYSE, Amex and NASDAQ (EXCHC codes NYSE Alter, NYSE Amex, NYSE

Arca, NYSE MKT, Nasdaq). We use only primary offerings, since these are the ones linked

to inflows of capital to the firm24. Following Lee, Lochhead, Ritter and Zhao (1996), we

compute the total costs of an issue as a percentage of the proceeds as follows:

total cost = GPCTP + EXPTH ∗ 10/PROCDS (58)

where the first item (GPCTP ) is gross spreads (management fees, underwriting fees, and

selling concession); and the second item (EXPTH∗10/PROCDS) are other direct expenses

(registration fee, printing,legal and auditing costs) as percentage of the proceeds .

Appendix C. Robustness

Our baseline economy assumes that productivity follows a geometric Brownian Motion. We

now evaluate the robustness of our results by assessing the output gains of eliminating

corporate income taxes in an economy in which productivity follows an AR(1) process. This

specification is the one used by Gourio and Miao (2010) in their study of the effects of

dividend taxation. In the next draft of the paper, we plan to further sensitivity analysis.

24 Secondary offerings are offerings of shareholders selling their existing shares, and therefore lead to noinflow of funds to the company.

37

Table 6: Summary Statistics SDC Platinum

Mean Median Std Dev. N

IPOGross Spreads 7.1 7 .16 1218Other Costs 4.0 3.0 2.9 994Total Costs 11.0 10.1 3.3 994

SEOGross Spreads 5.5 5.6 .2 1468Other Costs 1.5 0.8 2.2 1279Total Costs 7.0 6.6 3.0 1279

Calibration

The logarithm of productivity follows a diffusion process of the form:

dlnzt = −θlnztdt+ σdW (59)

which is the continuous time analog of an AR(1), where θ controls the mean reversion. From

Ito’s lemma, we obtain that

dzt = zt

(−θlnzt +

σ2

2

)dt+ σztdW. (60)

We assume that entrants draw productivity from the invariant distribution implied

by the process above, which follows a lognormal distribution with µ = exp(−θlnzt + σ2/2)

and variance σ2.25 We fix all parameters to the values in the baseline economy but for

the following parameters: (i) ψ, determining the magnitude of capital adjustment costs;

(ii) θ, determining the mean reversion of productivity; (iii) σ, determining the volatility of

productivity shocks; (iv) ξe, determining equity issuance cost when firms enter the economy.

We set θ = −log(0.76) = 0.2485 to match the an autocorrelation of shocks of 0.76, as

estimated in the Compustat data by Gourio and Miao (2010). The other three parameters

are calibrated by targeting (i) the volatility of the investment rate x/k across firms of 0.059,

(ii) the ratio of equity issuance by incumbent firms to investment of 12.6%, (iii) the fraction

of businesses with less than 100 employees of 53%.

The calibrated model economy with AR shocks matches well the calibration targets

(see Table 8). Relative to our baseline economy, the calibration requires higher variance

of shocks (0.50 instead of 0.15) and higher capital adjustment costs (0.18 instead of 0.09)

to match the volatility of investment rates and the fraction of small businesses. These

results are as expected: given that shocks are transitory we require a higher variance of

shocks to match the heterogeneity in business size; and given the higher variance of shocks

25Since Gourio and Miao (2010) do not model entry and exit of firms, the distribution of productivity intheir model economy is given by the invariant distribution of schocks.

38

Table 7: Calibration Baseline Economy with AR(1) growth

Parameter Description Valueψ Capital adjustment cost 0.18θ Mean reversion parameter 0.2485σ Volatility of prod. shock 0.5ξe Financing cost at entry 0.40

adjustment costs should also be larger in order to match the volatility of investment rates.

Moreover, the higher adjustment costs calibrated implies that the model economy requires

higher equity issuance costs at entry than in the baseline economy (0.40 instead of 0.30) to

match the fraction of investment financed with equity by incumbent firms. The intuition

is simple: when adjustment costs are large, firms want to do more investment at entry in

order to minimize adjustment costs after entry. Table 8 presents data in some non-targeted

dimensions showing that the economy with mean-reverting shocks performs worse than our

baseline economy. Relative to the data, the former model economy has a too low employment

growth of firms (0.01 instead of 0.02), a too high autocorrelation of (annual) investment rates

(0.71 instead of 0.57), and has almost no businesses with size bigger than 500 (while in the

data they represent about 10% of the total mass of businesses).

Results

Table 9 presents the aggregate long-run effects of replacing the corporate income tax with a

common tax on capital all forms of capital income (dividends, capital gains, interest income)

that raises the same amount of government revenue. We also report results for an experiment

in which the corporate income tax is reduced by a half (from 34% to 17%). The quantitative

findings are quite close to the ones in our baseline economy. Output increases by 15.5%

and capital by 39%, while in the baseline economy these figures were slightly lower (13.6%

and 35.2%). The elimination of corporate income taxation leads to a large increase in entry

47.7%, larger than the 39.3% increase in the baseline economy. The results are quite similar

when we consider reducing corporate income tax rates by a half. We thus conclude that are

key findings are robust to modeling productivity shocks as a mean reverting process.

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Table 8: Calibration Results

Data ModelTargetsVolatility investment rate 0.059 0.057Eq. issuance incumbents/investment 0.13 0.13Fract. bussinesses employees ∈ [50, 99) 0.53 0.52

Non-targeted dimensionsAvg. employment growth 0.02 0.01Autocorrelation invest. rate 0.57 0.71Agg. eq. issuance /agg. investment 0.13 0.13Dividend/ Earnings 0.098 0.46

Size Distribution of BusinessesNo. of Employees Fraction Data Fraction Model[50, 99) 0.53 0.52[100, 249) 0.29 0.45[250, 499) 0.089 0.03[500, 999) 0.0429 8e-7[1000, 2499) 0.0265 0[2500, 4999) 0.0099 0[5000,∞) 0.0115 0

Targeted moments in the data, and their respective counterpart in the model. Data comes from Com-

pustat, and BDS for the size distribution of businesses.

Table 9: Aggregate Effects of Eliminating Corporate Income Taxation under AR(1) ofshocks to growth of z.

Output Capital TFP Mass Entry Wage ττc = 0 15.5 39.0 6.2 47.7 15.5 0.38τc = 0.17 9.1 22.0 3.7 26.4 9.1 0.27

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